This brief paper sets out an underappreciated practically oriented paradox and its methodological implications. The paradox is highly relevant to central banks and any organization or agent that seeks to match or anticipate central bank policy, such as other actors in banking and finance. Specifically, there is a divergence between the statistical requirement of stationarity and any macroeconomic policy objective that involves a target that takes a consistent and positive value. This is not merely an esoteric issue of interest to statisticians. It has fundamental implications for policy contexts. When achieved, any policy target, such as inflation targeting, will necessarily result in a unit root. As such, an unintended consequence of successful policy is non-stationarity, which means policy is permanently seeking to actualise conditions that are at cross-purposes with typical analytical statistical requirements. The point and its significance are illustrated beginning with a simple AR model and artificial inflation dataset.